Guaranteed Cost Control For Large-Scale Descriptor Symmetric Systems

The basal idea of guaranteed cost control is to design a state feedback control taw such that the closed-loop systems are regular, stable, and impulse-free, while the cost index of the closed-loop systems is within a certain bound for all these admissible uncertainties. In recent years, there has been fully researched and obtained much work for the problem of guaranteed cost control with uncertain systems, along with the development of robust control of uncertain systems. However, so far the main work only in general systems. It is very hard to study the problem of guaranteed cost control for uncertain singular symmetric systems, owing to the particularity of the large-scale singular symmetric systems. So that it is of important practical meaning to study the problem of guaranteed cost control for large-scale uncertain singular symmetric systems.In this dissertation, a detailed analysis of the current situation of study on guaranteed cost control and a discussion about the problems of guaranteed cost control for large-scale singular symmetric composite systems and singular symmetric systems are stressed. The main results in this dissertation are as follows.Chapter 1 briefly introduces the problems in this paper, and gives the background about the research.In chapter 2, some attempt research about the guaranteed cost control of the large-scale singular symmetric composite systems is presented. First two modified lower-rank subsystems are given, which are equal to the original system. The design approach to a state feedback controller for the guaranteed cost is proposed, the closed-loop system provides a guaranteed cost and keeps regular, casual and stable for all admissible uncertainties. Furthermore it has upper bounds for the performance.In chapter 3, the resilient guaranteed cost control for singular symmetric systems with structured uncertainties is considered. Firstly, the sufficient condition in terms of LMIs for the existence of resilient guaranteed cost controllers is obtained for all the admissible uncertainties of systems and disturbances of controllers. Using the method of variable replacement to deal with the LMIs, we obtain the singular resilient dynamical output-feedback controllers. At last a numerical example is given to illustrate the designed method.In chapter 4, based on Riccati approach, the definitions of H∞guaranteed cost system and H∞guaranteed cost control are presented. The design approach to a state feedback controller for the guaranteed cost is proposed, the closed-loop system satisfies a given disturbance H∞performance y and provides a guaranteed cost and keeps regular, casual and stable for all admissible uncertainties. Under some conditions the H∞guaranteed cost controllers of the system can be obtained via LMI. Finally we give an example to demonstrate the feasibility and effectiveness of the result.Finally, a conclusion is given to summarize the thesis work.